This project aims to explain the neural mechanisms of breathing. Breathing in mammals consists of eupnea, periodic inspiratory pumping movements that draw air into the lungs for gas exchange, and sighs, larger less frequent breaths that periodically reinflate gas-exchange air sacs or express emotion, Eupnea and sigh rhythms are well coordinated and originate from the same set of brainstem neurons, but their underlying neural mechanisms remain incompletely understood. Using computational simulation and experimental tests of model predictions, this project will elucidate the mechanisms for eupnea and sigh rhythms in three SPECIFIC AIMS. In Aim 1, the project will ascertain the excitatory microcircuit dynamics for eupnea rhythm. An existing model of eupnea rhythm will be made mathematically tractable for geometric and bifurcation analyses, and its exclusive focus on synaptic dynamics will be augmented with biophysically realistic somatic membrane properties, In Aim 2, the project will explore the biochemical oscillatory mechanisms that give rise to sigh rhythm by developing and contrasting models of metabotropic signaling and intracellular Ca2+ oscillations that generate sigh-like network rhythm, In Aim 3, the project will examine the synaptic mechanisms that couple and coordinate the eupnea and sigh rhythms. Experiments will determine the synaptic transmission that coordinates eupnea and sigh, which will then constrain the models from Aims 1 and 2. This project will yield two deliverables of high intellectual merit: 1) an explanation of the cellular and synaptic mechanisms of eupnea- and sigh-related breathing rhythms, and ii) a biophysically realistic model for the core microcircuit that drives inspiratory breathing movements, both eupnea and sigh, suitable for inclusion within comprehensive models of the full behavior (e.g., with more motor phases and sensory feedback). Because rhythms are a ubiquitous aspect of brain function, the rhythmogenic mechanisms of breathing are of broad interest. This project will provide new knowledge regarding the cellular and synaptic neural origins of breathing that will inform the treatment and prevention of respiratory neuropathologies that afflict persons of all ages. The project will support STEM training of Ph.D. students and undergraduates, a thriving biomathematics consortium at William & Mary, and a summer internship program for public high schools, RELEVANCE (See instructions): Breathing consists of eupnea, regular breaths that pump oxygen into the lungs for gas exchange, and sighs, larger but less frequent breaths that reinflate gas-exchange air sacs or express emotion. This project applies mathematical models and experiments to explain how the mammalian brainstem generates breathing rhythms: eupnea and sigh. This knowledge will inform the treatment and prevention of respiratory neuropathologies that afflict persons of all ages from 'premies' to the elderly.